Much effort in modern semiconductor technology has been devoted to making devices that are capable of operating at high speeds. Such devices may be photodetectors, lasers, field effect transistors, etc. Some of this effort has been directed toward developing materials that should permit devices to operate at higher speeds by increasing the carrier velocity. For example, some Group III-V semiconductor compounds, such as gallium arsenide and indium gallium arsenide, have higher electron mobilities than does silicon. This should yield higher speed device operation at lower voltages because the electron drift velocity is a linear function of the electric field at low electric field values. Thus, the higher mobility leads to higher electron velocities at lower fields. Additionally, some Group III-V compounds have a longer mean free path for electrons than does silicon. As a result, under transient conditions electron velocities well in excess of the steady state velocity are obtained for short electrical lengths.
Some effort has also been directed toward developing new structures that are capable of high speed operation and have high carrier mobility. For example, modulation doped structures with high carrier mobility have been developed by Dingle et al and are described in Applied Physics Letters, 33, pp. 665-667, Oct. 1, 1978.
For purposes of discussion, the electron transport may be conveniently viewed as being of one of three types. The first type is collision dominated, and characterizes relatively long electrical lengths. This is a steady state behavior in which most, if not all, present day commercial semiconductor devices operate. The second type of transport is the ballistic type that characterizes very short electrical lengths. In this type, electrons are accelerated to the crystal limited velocity in a distance that is less than the mean free path for scattering and the electron velocity is derived from the potential drop. The third or intermediate type of transport is commonly termed "velocity overshoot". This is a transient type of transport in which the electron velocity exceeds the final velocity for a brief time period. Electron transport of these types are discussed in detail in Journal of Applied Physics, 48, pp. 781-787, February 1977. The study reported here assumed a uniform electric field and used the results of a Monte Carlo simulation of the electron transport properties to characterize velocity overshoot.
The physical mechanisms responsible for velocity overshoot may be briefly described. First, the rate of scattering of an electron is dependent on its energy in such a manner that once a threshold energy is exceeded, the scattering rate is enhanced considerably. In silicon or germanium, this enhancement is due to the onset of phonon emission which is an inelastic process. In compound semiconductors such as GaAs and InP this enhancement is due to the onset of quasi-elastic scattering to and from valleys of higher effective mass. Such scattering processes lead to lower average drift velocities than would have resulted in their absence. Such lower velocities are apparent in static steady state, i.e., velocity versus field curves, where velocity, having first increased linearly with electric field, saturates or even decreases at higher fields.
The second physical mechanism necessary for velocity overshoot is the time delay inherent in scattering processes, that is, their statistical nature and especially their Poisson character. Thus, it is possible to temporarily achieve high average drift velocities by abruptly increasing the electric field before the higher scattering rates have time to become fully effective in decelerating the electrons. Eventually, however, the higher scattering rates manifest themselves, first relaxing the excess momentum and then the excess energy.
One further aspect should be considered. If instead of applying the higher field indefinitely, the field is decreased back to its original value before the energy of most electrons exceeds the threshold for enhanced scattering, then the relaxation of this higher velocity will be advantageously delayed, being characterized by the lower relaxation rates associated with the lower field. In this manner the average velocity is enhanced over what it would have been had the field remained constant. The crucial physical parameter is the threshold energy for enhanced scattering, and the degree to which the electron's energy can be increased advantageously is limited by this threshold.
Although this nonsteady state electron transport, i.e., velocity overshoot, has been studied theoretically for a substantial period of time, for most of this time it was a theoretical curiosity because of the impracticality of realizing useful device structures due to the lack of suitable crystal growth techniques.
However, with the recent development of molecular beam epitaxy and the possibilities this growth technique offers for fabricating new structures, it has become possible to consider practical device structures that might utilize the nonsteady state electron transport. For example, L. F. Eastman discusses the use of planar doped barriers, i.e., layers that are highly doped, to rapidly accelerate electrons in a paper presented at The International Symposium on Gallium Arsenide and Related Compounds, Japan, 1981, pp. 245-250. However, these devices had only a single velocity overshoot with the second planar doped barrier layer being used to decelerate the electrons. As a result, the devices are useful only for very small, i.e., submicron, features.